SOLUTION: The length of a rectangle floor is 8 meter less than twice its width. If a diagonal of the rectangle is 20 meters, find the length and width of the floor.

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Question 166235: The length of a rectangle floor is 8 meter less than twice its width. If a diagonal of the rectangle is 20 meters, find the length and width of the floor.
Found 2 solutions by checkley77, Mathtut:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
L=2W-8
(2W-8)^2+W^2=20^2
4W^2-32W+64+W^2=400
5W^2-32W+64-400=0
5W^2-32W-336=0
(5W+28)(W-12)=0
W=12 M. IS THE WIDTH.
L=2*12-8=24-8=16 M. IS THE LENGTH.
PROOF:
12^2+16^2=20^2
144+256=400
400=400

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
L=length=2W-8 W=width diagonal makes to right triangles so
by the pathorean theorem %282W-8%29%5E2%2B%28W%5E2%29=20%5E2%29 multiply this out-simplify
5W%5E2-32W-336 using the quadratic formula we get W=12 and -5.6
throw out the negative value
so W=12 and L=2(12)-8=16